When exporting as .FBX, I don't have the option "include animation" that I've seen in tutorials
The following settings work for me with bridging Blender/UE4 but they may differ from engine to engine.  

Use 'Armature + Mesh' to transfer the model and its associated rigging.  

Use 'Armature' only to transfer subsequent animations.

Be sure to uncheck 'Add Leaf Bones' for UE4.  Other Engines may work best with this option activated.  A bit of trial and error should get you through that part.

Carefully go through the game engine created model/animation directory for what you imported and verify each new file to make sure they should be there, delete whatever mistakes happen from the transfer process.





If you happen to be using UE4, there is a video playlist published by Epic that shows how to handle these things on their end.

More info on the topic can be found using the following keywords:
"Unreal Engine, Youtube, Zak Parrish, Getting Started: Introduction to Blueprint 3rd Person Game Creation"

Here's a link to the playlist 

https://www.youtube.com/playlist?list=PLZlv_N0_O1gZS5HylO_368myr-Kg2ZLwb